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LinearAlgebra[Generic]

 MinorExpansion
 compute the determinant of a square Matrix by minor expansion

 Calling Sequence MinorExpansion[R](A)

Parameters

 R - the domain of computation, a commutative ring A - a square Matrix of values in R

Description

 • The (indexed) parameter R, which specifies the domain of computation, a commutative ring, must be a Maple table/module which has the following values/exports:
 R[0] : a constant for the zero of the ring R
 R[1] : a constant for the (multiplicative) identity of R
 R[+] : a procedure for adding elements of R (nary)
 R[-] : a procedure for negating and subtracting elements of R (unary and binary)
 R[*] : a procedure for multiplying elements of R (binary and commutative)
 R[=] : a boolean procedure for testing if two elements of R are equal

Examples

 > $\mathrm{with}\left(\mathrm{LinearAlgebra}[\mathrm{Generic}]\right):$
 > ${R}_{\mathrm{0}},{R}_{\mathrm{1}},{R}_{\mathrm{+}},{R}_{\mathrm{-}},{R}_{\mathrm{=}}≔0,1,\mathrm{+},\mathrm{-},\mathrm{=}$
 ${{R}}_{{0}}{,}{{R}}_{{1}}{,}{{R}}_{{\mathrm{+}}}{,}{{R}}_{{\mathrm{-}}}{,}{{R}}_{{\mathrm{=}}}{≔}{0}{,}{1}{,}{\mathrm{+}}{,}{\mathrm{-}}{,}{\mathrm{=}}$ (1)
 > R[*] := proc(f,g) expand(f*g) end: # polynomial multiplication
 > $A≔\mathrm{Matrix}\left(\left[\left[u,v,w\right],\left[v,u,v\right],\left[w,v,u\right]\right]\right)$
 ${A}{≔}\left[\begin{array}{ccc}{u}& {v}& {w}\\ {v}& {u}& {v}\\ {w}& {v}& {u}\end{array}\right]$ (2)
 > $\mathrm{MinorExpansion}[R]\left(A\right)$
 ${{u}}^{{3}}{-}{2}{}{u}{}{{v}}^{{2}}{-}{u}{}{{w}}^{{2}}{+}{2}{}{{v}}^{{2}}{}{w}$ (3)